Subgroup properties

In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.

subgroup invariant under conjugation

smallest normal subgroup by which the quotient is commutative

subgroup invariant under automorphisms of the parent group

subgroup such that there is a finite chain of subgroups of the group, each one normal in the next, from the original subgroup to the entire group

subgroup whose order is coprime to its index